What is (\partial)/(\partial x)(4sin(4x)e^{3x}) ?

The answer to (\partial)/(\partial x)(4sin(4x)e^{3x}) is 4(cos(4x)*4e^{3x}+e^{3x}*3sin(4x))

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(\partial)/(\partial x)(4sin(4x)e^{3x})

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

4 (cos (4 x) \cdot 4 e^{3 x} + e^{3 x} \cdot 3 sin (4 x))

Solution steps

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{\partial}{\partial x} (sin (4 x) e^{3 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (4 x), g = e^{3 x}

= 4 (\frac{\partial}{\partial x} (sin (4 x)) e^{3 x} + \frac{\partial}{\partial x} (e^{3 x}) sin (4 x))

\frac{\partial}{\partial x} (sin (4 x)) = cos (4 x) \cdot 4

\frac{\partial}{\partial x} (e^{3 x}) = e^{3 x} \cdot 3

= 4 (cos (4 x) \cdot 4 e^{3 x} + e^{3 x} \cdot 3 sin (4 x))

n = 1 \sum \infty \frac{5}{4 ^{n - 1}}

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}})

k = 1 \sum \infty e^{- k}

\frac{\partial}{\partial x} (4 x y arcsin (yz))

\int \frac{8}{9 t 81 t ^{2} - 64} d t

What is (\partial)/(\partial x)(4sin(4x)e^{3x}) ?
The answer to (\partial)/(\partial x)(4sin(4x)e^{3x}) is 4(cos(4x)*4e^{3x}+e^{3x}*3sin(4x))